Appearing as intricate crystalline structures and manifesting through delicate frost patterns, the Hoarbound Theorem is a mystical equation that governs the supernatural forces of winter. Its elegant yet complex formulas hold the secrets to decoding the ice phoenix's true purpose.

While not possessing a will of its own, the Hoarbound Theorem guides those who can decipher its frozen language, revealing insights that progress the investigation into the course's deepening mystery.